Answer

$-7\le k\le-3
$

Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
|k+5|\le2
,$ use the definition of absolute value inequality. Then use the properties of inequality to isolate the variable. Graph the solution.
In the graph a hollowed dot is used for $\lt$ or $\gt.$ A solid dot is used for $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Since for any $c\gt0$, $|x|\lt c$ implies $-c\lt x\lt c$ (or $|x|\le c$ implies $-c\le x\le c$), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-2\le k+5\le2
.\end{array}
Using the properties of inequality to isolate the variable results to
\begin{array}{l}\require{cancel}
-2\le k+5\le2
\\\\
-2-5\le k+5-5\le2-5
\\\\
-7\le k\le-3
.\end{array}
The graph above confirms the solution set of the inequality.